Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
using P = pair<int,int>;
#define int long long
signed main()
{
    int n;cin >> n;
    int a[n];
    rep(i,n)cin >> a[i];
    sort(a,a+n);
    double ab = a[n-1]+a[n-2];
    double ans = -1;
    rep(i,n){
        double cd = a[i+1] - a[i];
        if(i +1 == n-2)break;
        double res = ab/cd;

        ans = max(ans,res);



    }
    ans = max(ans,(double)(a[n-1]+a[n-4])/(a[n-2] - a[n-3]));
    ans = max(ans,(double)(a[n-3]+a[n-4])/(a[n-1]-a[n-2]));
    printf("%lf",ans);
    return 0;
}